We present an experimental investigation of the magnetic structure in a tetramer system SeCuO3 using neutron powder-diffraction and nuclear resonance techniques. We establish a commensurate antiferromagnetic ordering with a propagation vector k = (0, 0, 1). The order parameter follows a critical behavior near T-N = 8 K with a critical exponent beta = 0.32 in agreement with a three-dimensional universality class. Evidence is presented that a singlet state starts to form on tetramers at temperatures as high as 200 K, and its signature is preserved within the ordered state through a strong renormalization of the ordered magnetic moment on two nonequivalent copper sites m(Cu1) approximate to 0.35(mu B) and m(Cu2) < 0.8(mu B) at 1.5 K.